4.3 State observers and soft sensors

the activation function corresponds to the dynamic characteristics of the neuron transfer functions. The training algorithm refers to the parameter fitting procedure,

Feedforward networks (FNN) represent the simplest network configuration capable of describing the nonlinear behavior of bioreactors. In FFNs, neurons of each layer propagate their information to all neurons in subsequent layers. In each neuron, the input information corresponds to the weighted sum of all the outputs of the previous layer, and the weighting factors, weights and thresholds, are internally

Another type of ANNs frequently used is recurrent neural networks (RNNs). The structure of RNNs differ from FFNs, in the sense that some of the last layer neuron output signals are fed back as inputs to any previous layer. RNNs could converge to stable system solutions and include the effects of response delays. These characteristics make these models especially useful in the modeling of continuous

BBMs are based on the analysis of data generated to detect correlations, and basic functionalities between the variables and the WBMs are constructed from first principles. A hybrid model category between WBMs and BBMs is GBMs; these models implement a set of tools that combine some of the characteristics of both. Some of these characteristics include properties of process and control design, without losing the ability to explain the phenomena present in the system. Defining a parallel or serial data flow structure allows the integration of both, mechanistic

Parallel arrays are mainly used when there is a well-defined mechanistic model of the process and are suitable to improve its estimation performance. It is especially useful in cases where dynamic aspects of the system can be decoupled. Figure 2A shows a conceptual diagram of parallel interaction where the circle represents WBMs and the square BBMs, and the circle inside the square corresponds to a hybrid model. In the case of serial arrays, BBMs describe just specific terms of the WBMs, such as growth kinetics or transport parameters. Figure 2B represents the hybrid model where the BBMs (square) are substituted into the WBMs (circle). Stosch et al. presented a detailed panorama of this model [23]. In the design of bioreactors and their associated controllers, one of the difficulties is the determination of the kinetic model that adequately describes the growth rate of the respective microorganisms. The selection of a kinetic model leads to restrictive models for fixed operating conditions with little extrapolation possibility.

Classification of models as (A) parallel flow nonmechanistic model and (B) serial flow nonmechanistic model.

which provides the learning ability.

Current Topics in Biochemical Engineering

fitted for better system description [24].

and nonmechanistic information (e.g., Figure 2).

bioreactors [25].

Figure 2.

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4.2 Gray box models

Monitoring culture media requires the measurement of variables such as biomass concentration, substrates, dissolved oxygen, carbon dioxide, ammonia, and temperature, among others. These values are used for growth kinetics determination and bioreactor design. However, on multiple occasions, implementation of specific sensors is complicated, and there may be limitations in sensing frequency for variables such as biomass concentration. The implementation of indirect measurement methodologies, such as signal filtering, observer design, and ANNs, allows the estimation of some of these variables, and even the estimation of complex variables such as overall microbial growth rate and the heat flux produced by the system.

In control system theory, a major implementation of state observers is a common complementary strategy. These observers estimate some state variables that cannot be easily measured, either by the absence of suitable sensors, or because of low sampling frequency and high delay times. The main types of observers used for these purposes are those based on the Luenberger scheme, finite-dimensional observers, Bayesian estimators such as Kalman filters, interval observers, observers for fault detection, and even models of artificial intelligence such as ANNs and hybrid models [27].

State observer design requires that the estimated variables are detectable and observable. These states are observable if for a set of specific initial conditions, the internal states of the system are inferred from the knowledge of their outputs. Once its observability is determined, the observer can be designed; the desired type of observer is selected from categories mentioned above. Afterwards, tests of the estimator are carried out by comparing the real values against observer estimates, and in the case of important discrepancies between these values, the observer is adjusted or a different one is selected.

In the case of stirred tank reactors (batch, continuous, or semi-continuous), we may often assume that homogeneous conditions are available, so the system models obtained consist of aggregate parameter systems (ODEs). However, frequently in the case of tubular reactors or solid substrate fermentation systems, homogeneity assumptions are not adequate, so it is necessary to construct using distributed parameter models (PDEs). In the latter case, the design and performance of the main observers, such as Luenberger or Bayesian type, are usually limited, and therefore, it is usual to resort to another type of observer. In such a case, the observers based on a discretized system are substituted for traditional observers [28].

Soft sensors or virtual sensors are used as state observers in specific application. These soft sensors combine several physical measurements with dynamic characteristics to calculate other variables that are not measured.

Soft sensors can not only provide variable information to characterize a system but also facilitate the design of the control schemes.

In bioreactor design, soft sensors can be used to estimate unavailable variables such as biomass. Traditionally, biomass has been traditionally determined by use of a variety of methodologies such as optical density, dry weight, and microbial counts, among others. These techniques present several problems, the most important being the lack of continuous online measurements. To overcome this problem, various strategies have been applied, such as the implementation of low-cost sensors combined with signal processing strategies. For instance, the RGB sensor is used for biomass measurement in microalgae production reactors [29]. This type of sensors uses the intensity of the red, green, and blue (RGB) colors, which correlates with the biomass concentration using dry weight and/or colony formation unit (CFU) information, using the Beer-Lambert law principles. The correlation is described through linear fitting [30]. Additionally, it is possible to compensate background noise by use of ANNs even in the case of nonlinear correlation [31].

model is the basic logistic model incorporated with the Luedeking-Piret model (hybrid model) to describe the production of bioethanol from banana and pineapple

Fermentation: Metabolism, Kinetic Models, and Bioprocessing

DOI: http://dx.doi.org/10.5772/intechopen.82195

CFD simulations toward rational scale-down and design optimization [48].

Soft sensors are also useful in control design. For example, sliding mode observers can describe the behavior of sulfate reduction rate which results from Desulfovibrio alaskensis fermentation [53]. These observers use turbidimetric and

hydroxybutyrate production) [52].

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Another way to construct mathematical models of microbial growth is the use of FFNs, which describe the behavior of different configurations of bioreactors. An example of this type of applications is the modeling of the production of bioethanol obtained from sugar beets [49]. Here, a three-layer FFN is used to describe the dynamic behavior of the reactor. The first neuron layer consists of system inputs, which correspond to substrate concentration, substrate type, and fermentation time. The second layer corresponds to hidden neurons that process the information through their activation function. Finally, the third layer matches the output of the system that corresponds to the viable cell count of yeasts and the concentration of ethanol produced. On the other hand, GBMs and their hybrid models are not only used to characterize fermentation kinetics but can also describe general behaviors of bioprocesses. For example, in fed batch cultures of Chlorella pyrenoidosa, a hybrid scheme of ANN with mass balance mechanistic models describes the general behavior of the states of the system, reducing considerably the variability of their predictions, and achieving versatility in application [50]. These types of GBMs are useful in cases of high complexity due to metabolic dynamics of microorganisms [51]. GBMs or hybrid models are not only combinations of first principles with ANNs, but there may also be hybrid models obtained through the combination of statistical models with ANNs. This type of models usually has special applicability in the optimization of operating conditions of bioreactors (e.g., fed batch fermentation of Ralstonia eutropha for poly-β-

Cephalosporium acremonium (ATCC 36225) is one example of the utilization of SKMs where morphological differentiation and catabolite repression are the main aspects of the model approach [41]. SKMs can also effectively represent diauxic growth as well as the monitoring of an intracellular reactant in acetic acid production by Bacillus licheniformis [42]. Sansonetti reported a biochemically structured model for ethanol production from ricotta cheese whey by Kluyveromyces marxianus [43]. Wang studied a segregated kinetic model in fed-batch culture to represent simultaneous saccharification and co-fermentation (SSCF) for bioethanol production from lignocellulosic raw materials at high substrate concentrations [44]. Another interesting process is the solid-state fermentation. In most proposed models, a set of PDEs is used to describe how intraparticles are diffused or how the growth can be affected by intraparticle diffusion of oxygen, enzymes, hydrolysis products, and other nutrients and the role in the fermentation of other phenomena such as particle shrinkage and spatial microbial biomass distribution [45]. Computational fluid dynamics (CFD) provides information concerning the mixing modeling and design of bioreactors [46]. Another example of CFD is cephalosporin production by Acremonium chrysogenum; it was found that the oxygen transfer rate (OTR) directly affects fermentation performance with different impeller combinations [47]. Applications of CFD to fermentation modeling include effects of stress on cell morphology and mass transfer from the bulk solution to the organisms [46]. Biochemical models should be coupled to the CFD models in order to give a closed link between biochemistry and fluid dynamics of the system [33]. Haringa assesses the effect of substrate heterogeneity on the metabolic response of P. chrysogenum in industrial bioreactors via coupling of a 9-pool metabolic model with Euler-Lagrange

wastes [40].

Soft sensors can also be applied to nonexplicit system states. These observers can estimate lumped system variables, such as growth rate. As the simplest factor, temperature is commonly used, since it allows estimating system concentrations, due to intrinsic dependence between reaction rates and reaction enthalpy. The heat of reaction, either consumed or dissipated by the system, is one of the implicit system states used for reaction rate determination. The same strategy may also be used to determine microbial growth rates [32].

Microbial growth rates are inherently variable due to their metabolic nature and operation conditions. For example, as fluctuation in substrate concentration occurs in fed-batch bioreactors, the condition of osmotic pressure within cells is modified through the plasma membrane, which may change cellular energetics and the viability of cell division. A suitable strategy for these cases is the design of a substrate consumption rate observer. This kind of observer helps to design a robust control strategy against important fluctuations in maintaining constant substrate concentrations.

The use of observers or soft sensors is an interesting alternative to elucidate approximate values of system states, whether these are explicit or implicit, in cases where online continuous physical measurement is not available. These approximations can be used to design process control schemes that ensure proper functioning.
